Computers often include information storage systems having media on which data can be written and from which data can be read for later use. One form of information storage system is a disk drive. Disk drives use various types of media. One more common form is a drive unit incorporating one or more disks having a magnetic coating on the surface of the disk. Data is recorded in tracks which are subsections of the magnetic coating on the surface of the disk. Transducers are used to magnetize portions of the magnetic surface in a write operation. In digital magnetic recording systems, data are stored by writing a sequence of magnets with alternating polarity onto a medium using a write head (transducer). The binary ones and zeros of the stored data are represented either as the two possible magnetic polarities or the change or absence of change. Information is retrieved using a read head (transducer).
The read head and the write head are part of what is known as a data channel. The data channel handles data from a source, such as the computer, and writes it to a disk on a disk drive where it is stored for later retrieval. The data channel also handles reading individual magnetic transitions from the disk to retrieve that data previously stored. The data channel manipulates the readback signal produced by the read head (transducer) to produce a representation of the data previously stored. It should be noted that the read head and write head may be two separate transducers or may be a single transducer used for both reading and writing data.
The read head is configured such that a change in the polarity of the magnetization pattern results in a non-zero amplitude value in the transducer output. Because the read heads used in storage devices have a limited bandwidth, the response of the read transducer to a change in magnetization is a pulse with a non-zero width. Linear density is the number of bits of data that can be stored in a unit length of a track on the media. At linear densities of interest in present and future storage devices, the transition response pulse is sufficiently wide to add non-zero amplitude components to the signal in adjacent bit periods. This mechanism is known as intersymbol interference (ISI).
For reasons of convenience and practicality, the channel noise is assumed to be additive white Gaussian noise (AWGN). Gaussian or normal distributions are well known statistical models that accurately describe the thermal and electronics noise produced by the resistive component of the read transducer and the electronics of the preamplifier required to amplify the transducer output to usable levels. In terms of random variables, the term white indicates that observations of the random variable are uncorrelated; observations of a correlated random variable are said to be colored. Additive noise indicates that summing the noiseless signal s(t) and noise n(t) produces the received signal r(t)=s(t)+n(t), which implies that the signal and noise are uncorrelated.
A detector is also part of the data channel. The detector is the portion of the read channel that determines if a particular bit has a value of "1", which indicates a magnetic polarity in a first direction, or a "0", which indicates a magnetic polarity in a second direction. In earlier recording systems, data bits were detected by making a sample-by-sample decisions with a peak detection circuit, which made necessary the use of runlength limited (RLL) codes. This type of detector is called a peak detector. In terms of ISI, the function of the ISI code was to guarantee a minimum spacing between transitions so that the ISI components from adjacent transitions did not reduce the amplitude of the present transition below the detection threshold. Unfortunately, this technique is inefficient because it ignores the information content in the adjacent samples.
A second general type of detector is known as a sequence detector. Sequence detectors take advantage of the ISI terms by examining adjacent samples before making a decision. The Viterbi algorithm (VA) is an efficient means for implementing the maximum likelihood sequence detector (MLSD) which chooses the sequence that most likely produced the received or read signal. The complexity of the VA detector increases exponentially as the number of ISI terms increases. One type of magnetic storage device in use today overcomes this limitation by shaping the channel to produce partial response signals that have a predetermined and limited number of ISI terms. After shaping the channel response, a Viterbi algorithm is used to perform a maximum likelihood sequence detection. This type of sequence detector is known as a Partial Response Maximum Likelihood (PRML) detector. PRML detectors are commonly used in current information storage systems, such as disk drives.
PRML detectors have shortcomings. Several of the shortcomings result from the transition response being forced into something other than its natural shape. The performance of these partial response maximum likelihood (PRML) detectors also degrades as the channel response changes. The Viterbi detectors also become increasingly complex as the number of terms or samples used is increased.
Fixed delay tree search with decision feedback (FDTS/DF) performs sequence detection over a finite number of samples, generally less than the number of ISI terms. The unused ISI terms are subtracted by means of a nonlinear filter structure known as a decision feedback equalizer, which matches the shape of the unused tail of the channel response. Although FDTS/DF does not perform as well as the VA detector, it can outperform PRML schemes at high linear densities because the channel does not need to be shaped into a partial response form. An additional benefit of FDTS/DF is that the delay between the detector input and the decision is fixed and equal to the number of additional samples used in the decision process, i.e., if a total of three observation samples are used, the detector delay is .tau.=2. For a linear ISI channel with AWGN operating at a low bit error rate, FDTS/DF provides optimal detection for the implicit delay constraint. This is in contrast to MLSD which can outperform FDTS/DF because it has no delay constraint.
Signal space detection is similar to FDTS/DF in that it imposes a delay constraint of .tau. and employs a decision feedback equalizer. Unlike FDTS/DF which compares the received sample sequence against all possible sequences, the signal space detector (SSD) partitions a .tau.+1 dimensional space formed by the received samples into decision regions. In the general case, the partition boundaries can be nonlinear to accommodate non-Gaussian noise, but for Gaussian noise the partitions are formed by combining linear classifiers. Using linear classifiers with Gaussian noise, the optimal performance of the SSD matches that of FDTS/DF. A discussion of general signal space detection is given in a paper by B. Brickner et al. entitled "A signal space representation of fixed delay tree search for use with d=0 codes" from the Conference Record of the IEEE Globecom '95 Conference, Singapore, November 1995. A copy of this publication is attached hereto as Exhibit A and is expressly incorporated herein by reference.